Statistical Mechanical Models and Glauber Dynamics

Abstract

In recent years, mixing times of dynamics of statistical mechanical models have been the focus of much probability research, drawing interest from researchers in mathematics, physics, and computer science. The topic is both physically relevant and mathematically rich. But up to now, most of the attention has focused on particular models including rigorous results for several mean-field models. A few examples are (a) the Curie-Weiss (mean-field Ising) model [16, 17, 37], (b) the mean-field Blume-Capel model [20, 35], and (c) the Curie-Weiss-Potts (mean-field Potts) model [2, 13]. A good survey of the topic of mixing times of statistical mechanical models can be found in the paper by Cuff et al. [13].